Chapter 11.
Industry Productivity Measures
Background
IN THIS CHAPTER
S
tudies of output per hour in individual industries have
been part of the U.S. Bureau of Labor Statistics (BLS)
program since the 1800s. Prompted by congressional
concern that human labor was being displaced by machinery,
a study of 60 manufacturing industries was released as “Hand
and Machine Labor” in 1898. This report provided striking
evidence of the savings in labor resulting from mechanization
in the last half of the 19th century. The effects of productivity
advances upon employment remained an important focus of
BLS throughout the 1920s and 1930s. During this period, the
Bureau also began publishing industry indexes of output per
hour, which were based on available production data from
the periodic “Census of Manufactures” and employment
statistics collected by BLS.
In 1940, Congress authorized BLS to undertake continuing studies of productivity and technological changes. The
Bureau extended earlier indexes of output per hour developed by the National Research Project of the Works Progress Administration, and published measures for selected
industries. This work, however, was reduced in volume
during World War II, owing to the lack of meaningful production and employee hour data for many manufacturing
industries.
With the arrival of World War II, the program began to
focus on the most efficient use of scarce labor resources.
BLS undertook a number of studies of labor requirements for
defense industries, such as synthetic rubber and shipbuilding.
After the war, the industry studies program resumed on a
regular basis and was supplemented by a number of industry
studies based on the direct collection of data from employers.
Budget restrictions after 1952 prevented the continuation
of direct collection of data. Consequently, the preparation
of industry measures was largely limited to those industries
where data were readily available.
More recently, labor productivity growth has been
recognized as an important indicator of economic progress
and as a means to higher income levels. Interest in productivity
trends has also been heightened by other factors, including
public interest in the effects of technology and innovation
on economic growth and concern over increasing foreign
competition and domestic labor’s share of that growth.
Over the years, the Industry Productivity Program has
incorporated refinements in production theory and index
number theory and has expanded the number of series it
produces. In 1987, the program published the first multifactor
Background...................................................................
Labor productivity measures.........................................
Concepts...........................................................
Methods and data sources......................................
Output...............................................................
Labor input........................................................
Unit labor costs.................................................
Multifactor productivity measures................................
Concepts...........................................................
Methods and data sources......................................
Output...............................................................
Labor input........................................................
Capital...............................................................
Intermediate purchases.....................................
Weights for major input components . .............
Presentation...................................................................
Uses and limitations......................................................
Technical References....................................................
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productivity measures for detailed industries. These measures
relate output to combined inputs of capital, labor, energy,
materials, and purchased services. In 1995, following a
careful review of its methods and the economic literature,
the program released labor productivity measures that
incorporated an annual chain-weighted index for measuring
changes in industry output. The Tornqvist index aggregates
the growth rates of various industry outputs with annual
weights based on the products’ shares in total value of
industry production. In 1999, the program published industry
unit labor cost measures for the first time. These measures
reflect the relationship between labor compensation and real
output.
In 1998, the program completed a major industry expansion, increasing coverage from 180 industries to more than
500, as defined by the Standard Industrial Classification (SIC)
system. In 2000, industry multifactor productivity measures
were expanded to cover all 140 three-digit SIC manufacturing industries. Industry labor productivity measures were
converted from the SIC system to the North American Industry Classification System (NAICS) in 2003, and industry
multifactor productivity measures were converted from SIC
to NAICS in 2007. Efforts to expand industry coverage in
the service sector continue. In 2009, the program expanded
coverage of labor input measures to include all three- and
four-digit NAICS industries.
1
The Tornqvist formula yields the ratio of output in a given
year to that in the previous year. The ratios arrived at in this
manner then must be chained together to form a series. If
t = 3 and the base year is denoted by o, then
Labor productivity measures
Concepts
Labor productivity measures describe the relationship
between output and the labor time involved in its production.
Annual labor productivity measures are available starting in
1987 for most covered industries.
To calculate a labor productivity index, an index of
industry output is divided by an index of hours:
where
Qt
Qo
÷
Lt
Lo
Qt
The resulting chained output index, Qo , is used in the
productivity formula. The all-person-hour index for an
industry with multiple products is calculated in the same
manner as in the single-output case.
Qt
= the index of output in the current year,
Qo
Lt
Lo
Methods and data sources
= the index of labor input in the current year,
Output
Industry output is usually measured as a weighted index
of the changes in the various products or services (in real
terms) provided for sale outside the industry. Real output is
most often derived by deflating nominal sales or values of
production using BLS price indexes, but for a few industries
it is measured by physical quantities of output. Each of these
methods is discussed in turn.
t = the current year, and o = the base year.
For an industry producing a single uniform product or
service, the output index is simply the ratio of the number of
units produced in the current year divided by the number of
units produced in the base year. Similarly, the all-person-hour
index equals hours expended in the current year divided by
hours expended in the base year.
More typically, industries produce a number of different
products or perform a number of different services. For these
industries, output is calculated with a Tornqvist formula:
Deflated value output indexes. Deflated value output indexes
are derived from data on the value of industry output
adjusted for price change. The adjustment for price change is
accomplished by dividing the nominal value of output by one
or more price indexes. Nominal values are adjusted where
possible to reflect the total value of industry output from both
employer and nonemployer firms and to remove sales between
establishments in the same industry. Industry revenues or
production values are distributed to detailed output categories
and “deflated” at that level with detailed producer price
indexes (PPIs) or consumer price indexes (CPIs) produced
by BLS. Where possible, deflated value output indexes are
Tornqvist aggregations of the deflated values of individual
products or services. The resulting output indexes are
conceptually equivalent to indexes that are developed using
data derived from physical quantities of output.
For most manufacturing industries, sectoral value of
production is derived by removing intraindustry transfers
and resales from shipments and adjusting the shipments
for changes in inventory. Current-dollar industry value of
production is distributed to detailed primary product classes,
secondary products, and miscellaneous receipts based on
values of industry shipments and wherever-made shipments
collected in the U.S. Census Bureau’s “Annual Survey of
Manufactures” and “Census of Manufactures”.
For industries in retail trade and food services and drinking
places, current-dollar industry sales from the Census Bureau’s
“Annual Retail Trade Survey” are distributed to individual
product lines based on detailed data from the “Census of
Retail Trade.” Current-dollar sales for each product line are
deflated separately with appropriate BLS price indexes—
 n

q 
Qt
= exp ∑ wi ,t  ln i ,t 
Qt −1
 qi ,t −1 
 i =1
where
Qt
= the ratio of output in the current year (t) to the Qt −1
previous year (t-1),
n = number of products, ln
q i ,t
= the natural logarithm of the ratio of the quantity
of product i in the current year to the quantity in the
previous year, and
q i ,t −1
wi ,t = the average value share weight for product i.
The average value share weight for product i is computed
as:
where
Qt Q3  Q3  Q2  Q1 
=
=    
Qo Qo  Q2  Q1  Qo .
wi,t = (si,t + si,t -1) ÷2
s i ,t = pi ,t qi ,t

÷


n
∑
i =1

pi ,t qi ,t 


and p i ,t = price of product i at time t.
2
usually CPIs, but PPIs are used in some cases. For some
product lines, weighted combinations of two or more price
indexes are used.
For industries in wholesale trade, sectoral output is measured by deflating current-dollar revenues that have been
adjusted to remove intraindustry sales. Current-dollar industry sales from the Census Bureau’s “Monthly and Annual
Wholesale Trade Survey” are distributed to individual product lines based on detailed data from the “Census of Wholesale Trade.” Current-dollar revenues are deflated separately
for each detailed product line using appropriate PPIs from
BLS or price deflators from the Bureau of Economic Analysis (BEA).
Deflated value output for most other service industries
is measured by deflating current-dollar revenues from the
Census Bureau’s “Service Annual Survey” and “Census of
Service Industries.” Nominal values are deflated at the most
detailed level possible, with PPIs or CPIs from BLS. For most
industries, the deflated revenues are then combined using the
Tornqvist formula described above.
with no distinction made between hours of different groups of
employees. The labor input indexes are developed by dividing
aggregate hours for each year by the base-period aggregate.
Data Sources. Labor input measures are based primarily on
data from two BLS surveys. The primary source of data is
the Current Employment Statistics (CES) survey. The survey
collects monthly data on total paid employment by industry,
as well as data on employment and average weekly hours
for production workers in goods-producing industries and
for nonsupervisory workers in service-providing industries.
Historically, the CES survey provided estimates of average
weekly hours of only production and nonsupervisory workers,
but the survey has now begun collecting information on the
average weekly hours of all employees.
The Industry Productivity Program estimates average
weekly hours of nonproduction workers and supervisory
workers using data from the Current Population Survey
(CPS) in conjunction with the CES data. Annual relationships
between nonproduction (supervisory) worker average weekly
hours and production (nonsupervisory) worker average
weekly hours calculated from CPS data are applied to the
annual CES production (nonsupervisory) worker average
weekly hours for each industry. The CPS data also are used
to estimate the number and hours of the self-employed and
unpaid family workers.
CES and CPS data are available for most three- and
four-digit NAICS industries. BLS Quarterly Census of
Employment and Wages (QCEW) data or Census Bureau
nonemployer or small-firm data are used together with the
CES and CPS data when needed to derive detailed industry
estimates.
Although the employment and hours of all persons are
usually based on CES and CPS survey data, estimates for
some industries are derived from other sources. Estimates
for industries in the farm sector are based on data from
the U.S. Department of Agriculture, and measures for
industries in the nonfarm agriculture sector are based primarily
on data from the QCEW and the CPS. For mining industries,
estimates of nonproduction worker hours are derived from
data collected by the Mine Safety and Health Administration.
Labor input measures for total air transportation are calculated
with data from the Bureau of Transportation Statistics
(BTS), U.S. Department of Transportation. For line-haul
railroads, labor input measures are derived with data from
the Surface Transportation Board (STB), U.S. Department
of Transportation, and supplemented with data from the
Association of American Railroads (AAR). Employment of
postal service employees is from the CES and the hours data
are from the U.S. Postal Service.
Physical quantity output indexes. Where possible, physical
quantity output indexes are Tornqvist aggregations of the
quantities of individual products. The basic data on quantities
generally reflect primary products for each industry, at the
most detailed level possible. Physical quantity output indexes
are used for a few industries mainly in mining, utilities, and
transportation, and for commercial banking and the postal
service industry.
Data Sources. Industry output indexes are prepared using
basic data published by various public and private agencies,
at the most detailed level possible. The economic censuses
and annual surveys of the U.S. Census Bureau, U.S.
Department of Commerce are the primary sources of data
used in developing deflated value output measures. Data
for physical quantity output measures come from a number
of data sources, including the U.S. Departments of Energy,
Interior, Transportation, and Agriculture, as well as from
the Federal Reserve Board, the Federal Deposit Insurance
Corporation, and the U.S. Postal Service. Data from trade
associations also are used for some industries.
Labor input
Labor input reflects the total annual hours of all persons in
an industry. Indexes are prepared for all three- and four-digit
NAICS industries and for the government sector, as well
as for other industries for which productivity measures are
published. Employment and hours of all persons include
those of paid employees, the self-employed (partners and
proprietors), and unpaid family workers (persons who
work in a family business or farm without pay for 15 hours
a week or more). Total annual hours for each industry are
estimated separately for each class of worker as the product
of employment, average weekly hours, and the number of
paid weeks per year. The annual hours of each class of worker
are then aggregated to derive total industry hours. Hours of
all persons at the industry level are treated as homogeneous,
Unit labor costs
Unit labor costs represent the cost of labor required to produce
one unit of output. The unit labor cost indexes are computed
by dividing an index of industry labor compensation by an
index of real industry output. Unit labor costs also describe
the relationship between compensation per hour and real
output per hour (labor productivity). Increases in hourly
3
compensation increase unit labor costs, while increases in
labor productivity offset compensation increases and lower
unit labor costs.
Compensation, defined as payroll plus supplemental
payments, is a measure of the cost to the employer of
securing the services of labor. Payroll includes salaries,
wages, commissions, dismissal pay, bonuses, vacation and
sick leave pay, and compensation in kind. Supplemental
payments include legally required expenditures and payments
for voluntary programs. The legally required portion consists
primarily of Federal old age and survivors’ insurance,
unemployment compensation, and workers’ compensation.
Payments for voluntary programs include all programs not
specifically required by legislation, such as the employer
portion of private health insurance and pension plans.
si,t = pi,t xi,t
∑ (pi,txi,t)
pi,t = price of input xi in period t.
Since the growth rates are represented by differences in
logarithms, the antilogs of the differences must be chained to
form the index of multifactor productivity.
Methods and data sources
Output
The output measures are the same as those used in
calculating labor productivity.
Data Sources. For service-providing, mining, and utility
industries, labor compensation is derived using annual wage
data from the QCEW published by BLS along with data on
employer costs for fringe benefits from the Census Bureau
and the BEA. For industries in manufacturing, annual payroll
and fringe benefit data from the Census Bureau are used.
Labor input
The labor input measures are the same as those used in
calculating industry labor productivity. Industry labor input
is based on the total hours of all persons, and it is not adjusted
for composition change as are the labor input series that
BLS uses for private business and private nonfarm business
multifactor productivity measures.
Multifactor productivity measures
Concepts
The industry multifactor productivity indexes calculate
productivity growth by measuring changes in the relationship
between the quantity of output produced by an industry and
the quantity of inputs consumed in producing that output,
where measured inputs include capital and intermediate
purchases (including raw materials, purchased services, and
purchased energy) as well as labor input.
Multifactor productivity is derived as the difference between
the growth rate of output and the growth rate of a Tornqvist
index of capital, labor, and intermediate purchases inputs:
Capital
The measure of capital input is based on the flow of services
derived from the stock of physical assets. Physical assets are
the equipment, structures, land, and inventories used in the
production process. Financial capital is excluded. Capital
services are estimated by calculating real capital stocks.
Changes in the stocks are assumed proportional to changes
in capital services for each asset. Stocks of different asset
types are Tornqvist aggregated, using estimated rental prices
to construct the weights for assets of different types.
Capital is composed of numerous different assets
purchased at different times. Asset detail includes 25 types
of equipment, 2 types of nonresidential buildings, 3 types of
inventories (by stage of processing), and land. The measure
of capital for each year includes that year’s investment
in an asset plus the remaining productive stock from all
previous years’ investments. Capital stocks of equipment
and structures for each industry are calculated using the
perpetual inventory method, which takes into account
the continual additions to and subtractions from the stock
of capital as new investment and retirement of old capital
occur. Real (constant dollar) investments in various assets
are estimated by deflating current dollar investments with
appropriate price deflators. The perpetual inventory method
measures real stocks at the end of a year equal to a weighted
sum of all past investments, where the weights are the
asset’s efficiency relative to a new asset. A hyperbolic ageefficiency function is used to calculate the relative efficiency
of an asset at different ages.
 A 
 Q    K 
 L 
 IP 
ln t  = ln t  −  wk  ln t  + wl  ln t  + wip  ln t 
 Qt −1    K t −1 
 Lt −1 
 IPt −1 
 At −1 
where
wi= (si,t + si,t-1 )
2
ln = the natural logarithm of the variable,
A = multifactor productivity,
Q = output,
K = capital input,
L = labor input,
IP = intermediate purchases input, and
wk, wl, wip= cost share weights.
The input cost share weights are two-year averages of the
cost shares for each input (capital, labor, and intermediate
purchases, respectively), in years t and t-1, where
4
The hyperbolic age-efficiency function can be expressed
The internal rate of return is derived using data on property
income. Total property income is estimated for each industry
by subtracting the value of labor and intermediate purchases
from the value of output.
This method of calculating rental prices is similar to that
used in calculating multifactor productivity for major sectors
of the economy, except that no attempt is made to incorporate
the effects of indirect business taxes, for which data are
lacking at the industry level.
Rental prices are expressed in rates per constant dollar
of productive capital stocks. Each rental price is multiplied
by its constant-dollar capital stock to obtain asset-specific
capital costs, which are then converted to value shares for
Tornqvist aggregation.
as
St = ( L – t ) / ( L – ( B )t)
where
St = the relative efficiency of a t-year-old asset,
L = the service life of the asset,
t = the age of the asset, and
B = the parameter of efficiency decline.
The service life of the asset for each cohort of each type of
equipment and structure is assumed to be normally distributed
around an average service life for that asset type. For most
assets, these service lives are the same across all industries.
The parameter of efficiency decline is assumed to be 0.5 for
equipment and 0.75 for structures. These parameters yield a
function in which assets lose efficiency more slowly at first,
and then lose efficiency more rapidly later in their service
lives.
Current-dollar values of inventory stocks are calculated
for three separate categories of manufacturers’ inventories:
finished goods, work in process, and materials and supplies.
Inventory stocks for each year are calculated as the average
of the end-of-year stocks in years t and t-1 to represent the
average used during the year as a whole. Current-dollar
inventory values for the three categories of inventories are
deflated with appropriate price indexes.
Land stocks are estimated as a function of the movement
in constant-dollar net structures stocks for each industry.
Data sources. For manufacturing industries, capital indexes
are developed from data published and maintained by the
Census Bureau and BEA. Price indexes for different asset
categories are derived from PPIs developed by BLS. For air
transportation, capital measures are derived using data from
BTS, BEA, and the Air Transport Association (ATA). For
line-haul railroads, data from STB and Amtrak are used.
Intermediate purchases
The index of intermediate purchases is a Tornqvist index of
separate quantities of materials, services, fuels, and electricity
consumed by each industry. Except for electricity consumed
by manufacturing industries, for which direct quantity and
price data are available, the quantities are estimated by
deflating current-dollar values.
Constant-dollar materials consumed are derived by
dividing the annual industry purchases by a weighted price
deflator. Materials deflators are constructed for each industry
by combining detailed PPIs and import price indexes from
BLS using weights derived from the BEA benchmark inputoutput tables. Aggregate price indexes for deflating purchased
business services are constructed in a similar manner.
Annual total fuels consumed by each industry also are
deflated with weighted price deflators. PPIs for individual
fuel categories are weighted together with weights reflecting
detailed fuels expenditures by industry from the Energy
Information Administration (EIA), U.S. Department of
Energy.
Weights. The various equipment, structure, inventory, and
land stock series in constant dollars are aggregated into
one capital input measure using a Tornqvist index formula.
Capital stocks multiplied by rental prices are used to estimate
the cost share weights. Rental prices are calculated for each
asset as
RP =[( P x R ) + ( P x D ) – ( pt – pt–1 )] x (1 – uz – k ) / (1 – u)
where
RP
P
R
D
=
=
=
=
the rental price,
the deflator for the asset,
the internal rate of return,
the rate of depreciation for the asset, and
Data sources. For manufacturing industries, nominal values
of materials, fuels and electricity, and quantities of electricity
consumed by each industry are based on annual data from the
economic censuses and annual surveys of the Census Bureau.
To avoid double counting, estimates of materials consumed
by each industry are adjusted to exclude the value of materials
transferred between establishments in the same industry. The
values of purchased business services are estimated using
benchmark input-output tables and annual industry data from
BEA and the Census Bureau.
For air transportation, source data on cost of materials,
services, fuels, and electricity from the BTS are deflated
using cost indexes from ATA. For line-haul railroads,
P t - P t-1 = the capital gain term representing the price
change of the asset between years t and t-1.
(1 - uz - k)/(1 - u) reflects the effects of taxation where
u = the corporate tax rate,
z = the present value of $1 of depreciation deductions, and
k = the effective investment tax credit rate.
5
estimates from the STB are supplemented with data from
other sources including AAR, Amtrak, EIA, and the Edison
Electric Institute. The nominal values are deflated with PPIs
from BLS and implicit price deflators from BEA.
costs. Trends in unit labor costs shed light on the relationship
between labor productivity, hourly compensation, and
the cost of production. These data are used to assess the
changing efficiency, cost structure, and competitive position
of individual industries.
The measures of output per hour are subject to certain
qualifications. First, existing techniques may not fully take
into account changes in the quality of goods and services
produced. Second, although efforts have been made to
maintain consistency of coverage between the output and
labor input estimates, some statistical differences may
remain. Third, estimates of outputs and inputs for detailed
industries are subject to more volatility and error than
estimates for more aggregate sectors. Finally, year-to-year
changes in output per hour are irregular and, therefore, are
not necessarily indicative of changes in long-term trends.
Conversely, long-term trends are not necessarily applicable
to any one year or to any period in the future. Because of
these and other statistical limitations, these indexes cannot
be considered precise measures; instead, they should be
interpreted as general indicators of movements of output per
hour.
The measures of output per hour relate output to only
one input—labor time. They do not measure the specific
contribution of labor, capital, or any other factor of
production. The measures reflect the joint effect of a number
of interrelated influences such as changes in technology,
capital per worker, capacity utilization, intermediate inputs
per worker, layout and flow of material, skill and effort of the
workforce, managerial skill, and labor-management relations.
Indexes of multifactor productivity are subject to many
of the same limitations previously mentioned, with the
exception of the effects of changes in the ratios of other factor
inputs to labor. The construction of multifactor productivity
measures permits an analysis of the effects of the changes
in capital per hour and intermediate purchases per hour on
output per hour. Labor productivity is related to multifactor
productivity in the manner given by the following formula:
Weights. The separate indexes of real materials, services,
fuels, and electricity are aggregated into a total intermediate
purchases index using the Tornqvist formula. The weights
for each component are derived by dividing the currentdollar cost of each by the total combined cost of intermediate
purchases, and averaging these weights at times t and t-1.
Weights for major input components
The indexes representing quantity change for each of
the three major inputs—capital, labor, and intermediate
purchases—also are combined using the Tornqvist formula
to create an index of combined inputs. The relative weights
for each year are derived from the total cost for each input.
Labor compensation is used for the labor weight. The sum
of current-dollar values for materials, services, fuels, and
electricity constitute the weight for intermediate purchases.
The weight for capital is derived as a residual, by subtracting
the costs of labor and intermediate purchases from the total
value of output. The cost shares are averaged at time t and t-1.
Presentation
Annual BLS industry labor productivity measures are published in the Productivity and Costs by Industry news releases.
Annual indexes of output per hour also are published in the
Monthly Labor Review and rates of change are published in
the Statistical Abstract of the United States. News releases
and data tables can be accessed online by visiting the Labor
Productivity and Costs Web site at http://www.bls.gov/lpc/.
Industry multifactor productivity measures are published in
the Multifactor Productivity Trends for Detailed Industries
news releases, and can be accessed online by visiting the Multifactor Productivity Web site at http://www.bls.gov/mfp/.
Uses and limitations
  K 
 Q 
 L 
 A 
 L 
ln t  − ln t  = ln t  + wk ln t  − ln t 
 Qt −1 
 Lt −1 
 At −1 
 Lt −1 
  K t −1 
.
  IP 
 L 
+ wip ln t  − ln t 
 Lt −1 
  IPt −1 
.
Measures of industry output per hour are useful for
tracking changes in productive efficiency and the effects of
technological improvements in particular industries over time
or to compare performance among industries. Individuals
and companies also use these data as benchmarks to compare
against their firms’ performances.
Industry productivity series also are used to explain the
sources of productivity growth in the aggregate economy.
Industry productivity trends provide information that
helps researchers and policymakers better understand how
industries and sectors contribute to aggregate productivity
growth. Industry productivity analysis also can provide
information to assess the impact of policy changes or external
shocks on particular industries, and the resulting impact on
economic growth of the larger economy.
Unit labor costs are used to analyze trends in production
The above equation shows that the rate of change in labor
productivity (on the left side of the equation) is equal to the
change in multifactor productivity plus the effects of factor
substitution; that is, the combined effects of changes in the
weighted capital-labor ratio and the weighted intermediate
purchases-labor ratio (which are represented on the right side
of the equation). Conversely, the equation also shows that
the change in multifactor productivity equals the change in
labor productivity, adjusted to remove the weighted changes
in capital and intermediate purchases relative to labor.
6
Technical References
Duke, John and Lisa Usher. “BLS completes major expansion of industry productivity series,” Monthly Labor Review,
September 1998, pp. 35–51. Available online at http://www.
bls.gov/opub/mlr/1998/09/art4full.pdf.
Kunze, Kent, Mary Jablonski, and Virginia Klarquist.
“BLS modernizes Industry Labor Productivity Program,”
Monthly Labor Review, July 1995, pp. 3–12. Available online
at http://www.bls.gov/opub/mlr/1995/07/art1full.pdf.
Dumas, Mark, Brian Friedman, and Mark Sieling. “Labor
productivity in the retail trade industry, 1987–99”, Monthly
Labor Review, December 2001, pp. 3–14. Available online at
http://www.bls.gov/opub/mlr/2001/12/art1full.pdf.
Russell, Matthew, Paul Takac, and Lisa Usher. “Industry
productivity trends under the North American Industry Classification system,” Monthly Labor Review, November 2004,
pp.31–42. Available online at http://www.bls.gov/opub/
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